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All the ideas for 'fragments/reports', 'The Blank Slate' and 'Russell's Mathematical Logic'

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21 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / C. Structure of Existence / 2. Reduction
7508 Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker]
12. Knowledge Sources / D. Empiricism / 2. Associationism
7510 Connectionists say the mind is a general purpose learning device [Pinker]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
7513 Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker]
16. Persons / F. Free Will / 5. Against Free Will
7509 Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
7511 Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker]
7512 There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7505 Many think that accepting human nature is to accept innumerable evils [Pinker]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 2. Life
7516 In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
7515 All the evidence says evolution is cruel and wasteful, not intelligent [Pinker]
7514 Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker]